Research on pulsed magnetic fields dates back to the early 20th century. Nowadays, ultra-short pulsed magnetic fields are being utilized to better understand ultrafast physical microprocesses, such as domain motion and spin-orbit interaction, with time scales ranging from microseconds to femtoseconds. In particular, femtosecond magnetic field pulses are of great significance for studying ultrafast magnetization, ultrafast demagnetization, ultrafast magnetic storage, and spin ultrafast dynamics. However, traditional pulsed magnetic fields are limited by the performance of the pulse power supply and the mechanical strength of the coil and cannot achieve higher pulsed magnetic field strengths. Additionally, the pulse length of the magnetic pulse generated by the pulse power supply is at the millisecond level, which makes it unsuitable for studying faster magnetic dynamics processes. Fortunately, recent studies have shown that when ultra-short pulse lasers interact with plasmas, hot electrons are produced on the surface of the plasma target. These hot electrons are then excited and pass through the target material, producing strong charge separation on the back surface of the target material. Under the action of the laser, these excited electrons are accelerated, generating strong electromagnetic radiation. Consequently, using ultra-short pulse lasers to drive electron flows is currently the most promising method for generating femtosecond magnetic field pulses. Thus, the goal of this paper is to use a three-dimensional model to simulate the interaction between the driving optical field and the plasma target. This simulation will help to study the physical processes involved, such as the propagation of the optical field, the movement of free electrons, vortex currents, and pulse magnetic field generation. By optimizing the relevant parameters, this research aims to generate femtosecond magnetic field pulses.In this paper, we employ the Particle-In-Cell (PIC) method as our simulation approach. This method utilizes the Vlasov-Maxwell equation set to accurately describe the self-consistent dynamics in plasma simulation. The electrons in the plasma are subject to the Lorenz force, which generates new current density as they move. This equation effectively corrects the electric and magnetic fields through the charge density and current density. The driving light described is a circularly polarized vortex beam, with a wavelength of 800 nm and an optical field intensity of approximately 10¹⁶ to 10²¹ W/cm². The pulse width of the beam is roughly 10 fs. The plasma density ranges from 10¹⁸ to 10²⁰ cm^-3, and is confined within a cubic space with a side length of 30 λ₀. During the simulation process, we only consider refractive index changes due to electron density and do not account for non-linear effects. Additionally, we assume that the ions are stationary and that the initial velocity and temperature of the plasma are both 0.During theoretical simulation, a proportionality gradient between momentum potential and the strength of the light field is created due to the lowest intensity of the vortex beam at its center. This gradient then forms a potential well, preventing electrons from escaping outward and producing a structured electron beam with a femtosecond duration. In addition, particles acquire angular momentum in their radial motion within the laser field, generating a vortex current. This in turn produces a pulsed magnetic field based on the current magnetic effect.The simulation results indicate that when circularly polarized vortex beams, with light field intensities of the order of 10¹⁶ to 10²¹ W/cm², interact with plasma densities ranging from 10¹⁸ to 10²⁰ cm^-3, they can generate ultra-short magnetic pulses with peak intensities of 0.5~50 tesla and pulse time widths of about 10 fs. The effects of driving laser intensity and plasma density on these magnetic pulses are discussed through a simulated system calculation. The results show that the pulsed magnetic field intensity is proportional to the square root of both laser intensity and plasma density. Increasing electron density and laser intensity may facilitate the generation of ultra-short strong magnetic fields, providing numerical references for the production of femtosecond magnetic pulses in experiments.We expect that the simulation results above will facilitate the introduction of ultra-strong, ultra-short magnetic pulses into the femtosecond ultrafast realm, thereby supporting the advancement of research on ultrafast magnetic and spin dynamics, electronic motion and spin microprocessing control, ultrafast spin-electron magnetic storage applications, and magnetic switching.